Just pass the entire vagrant ssh-config as a config file to ssh with the -F configfile parameter. The host alias to connect to is defined on the first line in vagrant ssh-config; Host default means you can connect with ssh default.

I couldn't see an option to read the config file from the standard input, so went with the temp file route. Here's a one-liner that also cleans up the temporary $TMPDIR.vagrant-ssh-config file afterwards. It needs to be executed in the same directory as your Vagrantfile, assuming you vagrant box is up and running.

If you just want to set it up so you can use normal the normal ssh commandline, as well as scp and such, you can run vagrant ssh-config and append the output to your default ssh configuration. If you replace the line "Host default" with a more descriptive hostname, you should be good to go.

You can take any of the ssh-config arguments, and pass them to ssh on the commandline as -o Key=value. So, for a simple one-host vagrant setup (you might have to do a little more work with grep or perl for a multihost setup), you can do something like the following (or replace perl with sed if you want):

Vagrant stores the private key in ~/.vagrant.d/insecure_private_key and uses it to connect to every machine through ssh, considering that it is configured to connect on port 2200 (default) it would be something like:

ssh vagrant@localhost -p 2200 -i ~/.vagrant.d/insecure_private_key

Note: make sure that the private key is owned by the user running Vagrant.